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Relevant bibliographies by topics / Orthogonal Complement Spaces

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Journal articles

Academic literature on the topic 'Orthogonal Complement Spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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Journal articles on the topic "Orthogonal Complement Spaces"

1

Fricain, Emmanuel, Andreas Hartmann, and William T. Ross. "Range Spaces of Co-Analytic Toeplitz Operators." Canadian Journal of Mathematics 70, no. 6 (2018): 1261–83. http://dx.doi.org/10.4153/cjm-2017-057-4.

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AbstractIn this paper we discuss the range of a co-analytic Toeplitz operator. These range spaces are closely related to de Branges–Rovnyak spaces (in some cases they are equal as sets). In order to understand its structure, we explore when the range space decomposes into the range of an associated analytic Toeplitz operator and an identifiable orthogonal complement. For certain cases, we compute this orthogonal complement in terms of the kernel of a certain Toeplitz operator on the Hardy space, where we focus on when this kernel is a model space (backward shift invariant subspace). In the spi

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2

Narita, Keiko, Noboru Endou, and Yasunari Shidama. "The Orthogonal Projection and the Riesz Representation Theorem." Formalized Mathematics 23, no. 3 (2015): 243–52. http://dx.doi.org/10.1515/forma-2015-0020.

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Abstract In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real Hilbert spaces. Furthermore, we defined the continuity and the Lipschitz the continuity of functionals on real Hilbert spaces. Referring to the article [15], we also defined some definitions on

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3

Dragomir, Silvestru Sever. "Some Bessel type additive inequalities in inner product spaces." Studia Universitatis Babes-Bolyai Matematica 66, no. 2 (2021): 381–95. http://dx.doi.org/10.24193/subbmath.2021.2.13.

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"In this paper we obtain some additive inequalities related to the cele- brated Bessel's inequality in inner product spaces. They complement the results obtained by Boas-Bellman, Bombieri, Selberg and Heilbronn, which have been applied for almost orthogonal series and in Number Theory."

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4

BHAT, B. V. RAJARAMA. "A COMPLETELY ENTANGLED SUBSPACE OF MAXIMAL DIMENSION." International Journal of Quantum Information 04, no. 02 (2006): 325–30. http://dx.doi.org/10.1142/s0219749906001797.

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Consider a tensor product [Formula: see text] of finite-dimensional Hilbert spaces with dimension [Formula: see text], 1 ≤ i ≤ k. Then the maximum dimension possible for a subspace of [Formula: see text] with no non-zero product vector is known to be d1 d2…dk - (d1 + d2 + … + dk + k - 1. We obtain an explicit example of a subspace of this kind. We determine the set of product vectors in its orthogonal complement and show that it has the minimum dimension possible for an unextendible product basis of not necessarily orthogonal product vectors.

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5

Ferreira, Milton, and Teerapong Suksumran. "Orthogonal Gyrodecompositions of Real Inner Product Gyrogroups." Symmetry 12, no. 6 (2020): 941. http://dx.doi.org/10.3390/sym12060941.

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In this article, we prove an orthogonal decomposition theorem for real inner product gyrogroups, which unify some well-known gyrogroups in the literature: Einstein, Möbius, Proper Velocity, and Chen’s gyrogroups. This leads to the study of left (right) coset partition of a real inner product gyrogroup induced from a subgyrogroup that is a finite dimensional subspace. As a result, we obtain gyroprojectors onto the subgyrogroup and its orthogonal complement. We construct also quotient spaces and prove an associated isomorphism theorem. The left (right) cosets are characterized using gyrolines (c

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6

Ferguson, Sarah H., and Richard Rochberg. "Higher order Hilbert-Schmidt Hankel forms and tensors of analytical kernels." MATHEMATICA SCANDINAVICA 96, no. 1 (2005): 117. http://dx.doi.org/10.7146/math.scand.a-14948.

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The symbols of $n^{\hbox{th}}$-order Hankel forms defined on the product of certain reproducing kernel Hilbert spaces $H(k_{i})$, $i=1,2$, in the Hilbert-Schmidt class are shown to coincide with the orthogonal complement in $H(k_{1})\otimes H(k_{2})$ of the ideal of polynomials which vanish up to order $n$ along the diagonal. For tensor products of weighted Bergman and Dirichlet type spaces (including the Hardy space) we introduce a higher order restriction map which allows us to identify the relative quotient of the $n^{\hbox{th}}$-order ideal modulo the $(n+1)^{\hbox{st}}$-order one as a dir

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7

Lee, Hyunjin, and Young Jin Suh. "Cyclic parallel hypersurfaces in complex Grassmannians of rank 2." International Journal of Mathematics 31, no. 02 (2019): 2050014. http://dx.doi.org/10.1142/s0129167x20500147.

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The object of the paper is to study cyclic parallel hypersurfaces in complex (hyperbolic) two-plane Grassmannians which have a remarkable geometric structure as Hermitian symmetric spaces of rank 2. First, we prove that if the Reeb vector field belongs to the orthogonal complement of the maximal quaternionic subbundle, then the shape operator of a cyclic parallel hypersurface in complex hyperbolic two-plane Grassmannians is Reeb parallel. By using this fact, we classify all cyclic parallel hypersurfaces in complex hyperbolic two-plane Grassmannians with non-vanishing geodesic Reeb flow. Next,

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8

Amerik, Ekaterina, and Misha Verbitsky. "Collections of Orbits of Hyperplane Type in Homogeneous Spaces, Homogeneous Dynamics, and Hyperkähler Geometry." International Mathematics Research Notices 2020, no. 1 (2018): 25–38. http://dx.doi.org/10.1093/imrn/rnx319.

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Abstract Consider the space M = O(p, q)/O(p) × O(q) of positive p-dimensional subspaces in a pseudo-Euclidean space V of signature (p, q), where p &gt; 0, q &gt; 1 and $(p,q)\neq (1,2)$, with integral structure: $V = V_{\mathbb{Z}} \otimes \mathbb{Z}$. Let Γ be an arithmetic subgroup in $G = O(V_{\mathbb{Z}})$, and $R \subset V_{\mathbb{Z}}$ a Γ-invariant set of vectors with negative square. Denote by R⊥ the set of all positive p-planes W ⊂ V such that the orthogonal complement W⊥ contains some r ∈ R. We prove that either R⊥ is dense in M or Γ acts on R with finitely many orbits. This

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9

Akritas, A. G., G. I. Malaschonok, and P. S. Vigklas. "The SVD-Fundamental Theorem of Linear Algebra." Nonlinear Analysis: Modelling and Control 11, no. 2 (2006): 123–36. http://dx.doi.org/10.15388/na.2006.11.2.14753.

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Given an m × n matrix A, with m ≥ n, the four subspaces associated with it are shown in Fig. 1 (see [1]).  Fig. 1. The row spaces and the nullspaces of A and AT; a1 through an and h1 through hm are abbreviations of the alignerframe and hangerframe vectors respectively (see [2]). The Fundamental Theorem of Linear Algebra tells us that N(A) is the orthogonal complement of R(AT). These four subspaces tell the whole story of the Linear System Ax = y. So, for example, the absence of N(AT) indicates that a solution always exists, whereas the absence of N(A) indicates that this solu

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10

Hudzik, Henryk, Yuwen Wang, and Ruli Sha. "Orthogonally complemented subspaces in Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (2005): e1701-e1711. http://dx.doi.org/10.1016/j.na.2005.02.002.

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